In my definition of sincere voting, I inadvertently left in the words "or ratings". I'd meant to take those words out, and have a definition that's only abour pairwise preferences. I was mistaken to say that, when optimal strategy is used with Point Ratings, that strategy is sincere by my definition. It isn't, because the voter is declining to express some preferences as described in the definition. That definition works fine for rank methods, and for Plurality & Approval. With Point Ratings, if you vote your sincere ratings, that registers as sincere by my definition. If instead, you use the optimal stratregy of voting as in Approval, that registers as insincere by that definition. The only way in which my definition would disagree with the strictest meaning of sincere voting in Point Ratings is when it calls your vote sincere as long as your voted ratings are in the same order as your sincere ratings, even if they aren't really the same. In that case, you're not voting insincerely enough for that definition to call it insincere. When yesterday I defined defensive strategy, I wanted to get rid of any possible ambiguity in the definitions that I'd previously been using. But, for a definition intended to apply to actual voting, it was probably unrealistic to use the term "the goal". That should be changed to "a goal", or "a wish". Or maybe avoid the issue of intent altogether by saying: Defensive strategy: Voting intended to defeat a certain candidate, on the part of members of a majority who all prefer a certain same other candidate to him. [end of definition] That's my definition of defensive strategy now. It's what I mean if I use that word in the future, and it's how I interpret it if anyone else uses that word, unless they've stated a different definition, as Markus has. I'm not changing my definition of offensive strategy from what it was yesterday. My new definition of defensive strategy makes reference to the people who have the power to defeat a candidate without reversing preferences. Mike Ossipoff _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Share information about yourself, create your own public profile at http://profiles.msn.com.